Thursday, December 7, 2023

Variance III

 

Casey Jones

Driving that train, high on cocaine Casey Jones, you'd better watch your speed Trouble ahead, trouble behind And you know that notion just crossed my mind

What if we are high on something other than cocaine?

The movie The Seven Percent Solution dealt with Sherlock Holmes addiction to a solution of seven percent cocaine.  The variance, σ2, of the universe with a mean choice of 0.5 appears to be 0.822467. But this is a complex number that is really 0.822467 + 0*i.  The zero coefficient of the imaginary axis means that it is zero, not that the imaginary axis does not exist. 

The solution for the Standard Deviation, σ, the square root of the variance, depends on whether it is solved on a flat, Euclidean, or on a hyperbolic surface.  On a flat surface, the Standard Deviation would appear to be 0.9069, which is 2.9% higher than the solution of  0.8807 on a hyperbolic surface.  Should we deal with our belief, addiction, that we live on a flat surface and admit that we might intead live in a hyperbolic universe?

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